Timber vs. Steel Bridge Superstructure Construction: A Simplified Structural, Economic and Environmental Analysis

Steel Bridge Superstructure Construction: A Simplified Structural, Economic and Environmental Analysis Jack Dugdale UVM College of Engineering and Mathematical Sciences, jdugdale@uvm.edu

University of Vermont

ScholarWorks @ UVM

2015

Timber vs Steel Bridge Superstructure

Construction: A Simplified Structural, Economic

and Environmental Analysis

Jack Dugdale

UVM College of Engineering and Mathematical Sciences, jdugdale@uvm.edu

Follow this and additional works at:http://scholarworks.uvm.edu/hcoltheses

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Recommended Citation

Dugdale, Jack, "Timber vs Steel Bridge Superstructure Construction: A Simplified Structural, Economic and Environmental Analysis"

(2015) UVM Honors College Senior Theses Paper 88.

Timber vs Steel Bridge Superstructure Construction

A Simplified Structural, Economic and Environmental Analysis

Jack Dugdale Advised by Eric M Hernandez, PhD

Acknowledgements

I would like to thank Professor Eric Hernandez for his help in understanding the various nuances of the AASHTO Standards as well as his general assistance with questions regarding structural analysis and SAP modeling I would also like to thank the rest of my thesis committee, Professors Donna Rizzo and Priyantha Wijesinghe, for their understanding and flexibility Finally, I would like to thank my family and my friends

Flora and Linnea for their support and encouragement

Abstract

For thousands of years, bridges were constructed primarily of timber Then, in 1779, the first cast iron bridge was built, followed by the first primarily steel bridge in 1874 By the 20thcentury, wood had fallen completely out of favor for all major infrastructure projects This thesis examined if such a wholesale shift to steel is still sustainable today given increased concerns about social and environmental impacts, particularly in light of modern advances in engineered wood products Focusing on single span highway bridges in Vermont, structural models were created to determine appropriate section sizes for functionally equivalent steel and glued laminated timber sections Methods for performing economic and embodied energy analyses were then proposed While final conclusions regarding the relative benefits of steel and timber were not reached, it is believed that this three-pronged approach will ultimately allow for a nuanced and multi-faceted view of the benefits and costs associated with each material, allowing for more informed infrastructure planning

Table of Contents

1 Introduction ……….1

1.1 History………1

1.2 Reasoning ……… ……2

1.3 Necessity and Hypothesis……… ….5

2 Literature Review ………6

3 Methodology …….……… 8

3.1 Bridge Design and Analysis ……….….8

3.2 Economic……… 25

3.3 Environmental ……… ……25

4 Results ………….………26

5 Conclusions ………28

6 References ……… 30

Appendix A: MATLAB Code for Calculating Design Vehicle Placement

Appendix B: Summary of ICE Database Embodied Energy Coefficients

Appendix C: ICE Database References

Appendix D: Vermont Agency of Transportation S-352 Standard Plans

This all changed with the coming of the Industrial Revolution and the widespread use of iron Iron was certainly not a new discovery, having been used by the Greeks, Romans and many others However, due to the difficulty in smelting large quantities of ore using charcoal, it had typically only been used for small objects such as pots, tools, weapons and armor Not until the early 1700’s was an efficient process for smelting iron ore using coal and later coke developed The lower cost and higher energy density of coal when compared to charcoal allowed for cheaper mass production of cast iron This sudden increase in supply, and associated decrease in cost, permitted the first cast iron bridge to be constructed in 1779 in Coalbrookdale, England Subsequent advances in metallurgy resulted in the Bessemer Process, which led to the widespread development of the steel industry and the construction of the first all steel bridge in

1874 over the Mississippi River at St Louis (Kirby et al., 1990) By the 20th century, the widespread availability of high quality steel meant that timber had fallen completely out of favor

as a structural material for use in bridges To this day, steel remains a dominant construction material Partly as a result, relatively little research has been performed regarding the advantages and disadvantages of wood as a construction material, resulting in a dearth of comprehensive information

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1.2 Reasoning

There are many very compelling reasons to utilize steel in both bridge and building construction As an engineered product, it has carefully controlled and well known properties that the designer or engineer can use with a reasonably high degree of confidence It is widely available in a multitude of sizes and shapes Furthermore, steel is very strong in both tension and compression, which makes it highly adaptable for various uses These advantages are well known and are some of the many reasons that steel has come to dominate the construction industry for large structures

However, there are also several notable disadvantages to using steel as well First, it is comparatively heavy, having a density of 490 lbs/ft3 (pcf) vs 140 to 150 pcf for concrete and about 35 pcf for softwood timber For comparison, water weighs 62.4 pcf This weight means that transportation costs and associated vehicle emissions may be significant Second, while steel itself is not uncommon, specialized tools are required in order to cut, handle, erect and connect steel members This can slow construction and increase project costs Third, though steel is economically inexpensive, it can have significant environmental impacts due to high energy requirements in the mining and manufacturing processes Finally, though it can be a durable material, steel can also experience significant corrosion when exposed to road salt, either alone

or in combination with vehicle emissions This scenario is quite common in northern regions of the United States (Houska, 2007)

Timber, in contrast to steel, is a naturally occurring material There is thus significant variation between individual wood specimens, even from within the same tree Knots and other defects can greatly alter the strength characteristics of the member Additionally, the sizes of trees themselves have historically limited what could be constructed of wood Unlike steel, which can be fabricated in any size desired, traditional timber products are directly limited by the size of the source tree With the exhaustion of the larger old growth forests, this has restricted the commercial use of wood to dimensional lumber, the ubiquitous 2x4’s and 2x6’s used in home construction While useful for many things, these small sizes are wholly unsuited to bridge construction

However, modern technology offers a solution to both of the aforementioned issues in the form of glued laminated timber, or glulams These are engineered wood products made by

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laminating together individual pieces of dimensional lumber using heat, pressure and glue to create large beams, as shown below in Figure 1 Typically, preservatives are also applied during the manufacturing stage to inhibit rot and decay

Figure 1: Example of a glulam beam prior to finishing (Source:

http://www.woodsfieldgroup.com/img/img-what.jpg)

Much like steel or concrete beams, glulam members can be made in practically any size desired, although longer lengths can present transportation and handling difficulties Furthermore, the lamination process helps to minimize the impact of defects in individual pieces of wood While a knot in a single 2x4 might prove critical when the member is stressed, by sandwiching that same member in amongst several other pieces of wood, the impact of that defect is minimized As a result, glulams tend to be more dimensionally stable and have more consistent structural properties than sawn timber

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Given the adaptability of glulams, it is not surprising that they have begun to be used to construct bridges These are typically short span bridges designed for pedestrians or light vehicular traffic, as depicted in Figure 2

Figure 2: Glulam pedestrian bridge (Source:

http://www.custompark.com/_images/products/bridges/glulam-beam-bridge-03.jpg)

However, larger designs capable of supporting normal vehicular traffic have also been constructed As described by the American Institute for Timber Construction, an industry trade group, “[w]ood’s ability to absorb impact forces created by traffic and its natural resistance to chemicals, such as those used for de-icing roadways, make it ideal for these installations” (AITC, 2007)

In addition to its structural properties, glued laminated timber also has the potential to have reduced environmental impacts in comparison to steel Steel, for all of its beneficial

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properties, is energy intensive to manufacture Even if recycled material is used (which it often is

in developed countries), it still must be melted at high temperatures in order to be formed into shapes Glulams, on the other hand, while certainly requiring more energy to produce than dimensional lumber, do not need to be subjected to processes which are as energy intensive as used in steel manufacturing Additionally, the source material itself, wood, is renewable, unlike iron, of which there is a finite amount The environmental impacts of the harvesting process itself depend on the techniques used, some of which are more harmful than others, but the trend

in recent years has been to promote more sustainable forestry practices Organizations such as the Forest Stewardship Council (FSC) have been created to certify forests as being sustainably managed

While the above description speaks to the potential benefits of using glulams, relatively little research has been conducted to date specifically comparing timber and steel construction, particularly as it applies to bridges There is therefore little concrete evidence as to whether or not either steel or glulam timber offers any concrete advantage over the other material This paper attempts to partially address that gap

1.3 Necessity and Hypothesis

According to an AP analysis of the 607,380 bridges included in the 2013 National Bridge Inventory, there are 65,505 structurally deficient bridges in the U.S There are also 20,808 bridges which are fracture critical, meaning that the failure of a single member can result in complete collapse A total of 7,795 bridges were labelled as being both structurally deficient and fracture critical (AP, 2013) This has led the American Society of Civil Engineers to give the nation’s bridges an overall grade of a C+ in its latest Report Card for America’s Infrastructure (ASCE, 2013)

There is clearly a need, therefore, for significant infrastructure improvements and the construction of numerous new bridges in the coming years Given this, as well as the natural desire of state and federal agencies to save money wherever possible, the importance of prompt replacement of deficient bridges and the growing interest in green building practices, it would be wise to consider all available construction materials for use in such projects However, while steel and concrete are well studied, timber has been little examined as a possible structural

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material for bridges The current focus on the state of America’s transportation network offers an opportune time to correct that oversight so that engineers and policymakers have accurate information on which to base decisions

The goal of this thesis is not to demonstrate that wood is a viable structural material in general The tens of thousands of wood frame buildings built every year, the historic post and beam structures and the miraculous engineering feats of ancient cultures leaves no doubt that it can be used quite effectively Nor is the purpose even to show that bridges specifically can be constructed from wood Many thousands of sophisticated bridges were made of wood in the past, and hundreds still exist to this day, spanning hundreds of feet and carrying modern traffic loads Instead, this thesis intends to examine whether, using modern engineered wood products, a

timber bridge can be competitive with a more typical steel girder bridge and offer a viable

alternative for the construction of new infrastructure It is theorized that timber is in fact a practical alternative to steel for bridge superstructures when all relevant factors are considered This thesis will attempt to compare the relative merits of steel and timber in three important categories: structural properties, economic cost and environmental impact Conclusions will then

be drawn regarding in which situations, if any, wood may be an appropriate material to utilize It

is anticipated that timber will offer the most benefits, both economic and environmental, in short bridges of less than 50 feet in length For longer spans, it is expected that the greater absolute strength of steel will permit the construction of more efficient structures with less material, reducing both cost and environmental impact

2 Literature Review

A tremendous amount has been written about the merits and properties of steel design, as well as its economic and environmental impact There is much less literature of note in regards to wood design in general or of bridges in particular The most comprehensive analysis thus far was performed by the U.S Forest Service in 1990 and primarily focuses on lightly travelled short spans used in National Parks Furthermore, the only environmental comparisons found between wood and steel focus primarily on residential and commercial structures, as opposed to infrastructure, and vary widely in their conclusions Therefore, a wide variety of resources were required in order to create a representative and useful knowledge base

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The structural properties of steel (AISC, 2013) and timber (NDS, 2015) have both been extensively researched and tabulated Multiple volumes list the properties of every conceivable material and section type which one might encounter In general, structural steel is available with yield strengths of 36 or 50 ksi (AISC, 2013) Wood, while more variable, depending on both the species and the loading orientation, typically has a design bending strength between 1.5 and 2.5 ksi (NDS, 2015)

In addition to extensive data on material properties, many specifications and codes have been developed governing the construction standards for steel bridges (FHWA, 2012) and bridges in general (AASHTO, 2012) There are fewer standards available specifically for wood bridges, but some useful information can be obtained from the experiences of the U.S Forest Service (USFS, 1990)

An economic analysis is naturally dependent on site specific conditions Depending on the proximity of the construction site to mills, factories, access points and other features, costs can vary significantly Labor costs also vary by region For this reason, it will be assumed that the bridges discussed in this study will be constructed in the vicinity of Burlington, Vermont Price estimation will then be based primarily on the five year averaged price list published by the Vermont Agency of Transportation (VTrans) The figures found in this table provide a rough guide to construction costs based on the amount of material needed for each component, allowing the initial cost of the project to be calculated These values, however, are based on data from projects of various sizes scattered throughout the state Thus, while they provide a useful approximation, actual costs will likely vary significantly depending on site specific conditions

The final element of analysis focuses on the relative environmental impact of each material choice There are multiple ways in which this can be measured, but for this analysis, the

embodied energy needed to produce each material will be the primary metric (For further detail

on this, please see the methodology section.) A great deal of research has been done on this subject, covering multiple materials and uses in many countries Due to the varying inputs (distance between resource and mill, amount of recycling, energy sources used for processing, type of transportation, boundaries of study, etc.), the calculated values for each material can vary tremendously, sometimes by orders of magnitude The data varies both between countries and

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regions as well as between researchers in the same country Nonetheless, this has only encouraged further study, so there is a plethora of available information on the subject

The single most comprehensive data set created to date, offering information on most

common structural materials, is the Inventory of Carbon and Energy (Hammond and Jones,

2011), which contains extensive and well documented numbers for every material Unfortunately, the study focused primarily on the UK and EU, so the data, particularly for timber, may not be fully applicable to an American analysis Further information is available from The United Kingdom (Harris, 1999), India (Reddy and Jagadish, 2003), New Zealand (Buchanan and Honey, 2003; Alcorn and Baird, 1996) and the United States (Griffin et al., 2010) On the whole, however, the majority of papers seem to come out of Europe and New Zealand, perhaps due to more restrictive carbon emission limits In general, all sources agree that steel has a higher embodied energy (typically around 20 MJ/kg) than wood (closer to 10 MJ/kg)

In addition to raw data focusing solely on the embodied energy of individual materials, several studies comparing materials have been conducted, primarily focusing on residential and commercial buildings The most relevant of these is perhaps one which focuses on French single family homes built with locally sourced material versus similar homes built with concrete (Morel

et al., 2010) The results of that study indicated that total energy consumption was reduced by 215% when locally sourced materials were used

3 Methodology

3.1 Bridge Design and Analysis

In order to effectively compare the benefits of steel and timber bridge superstructure construction, it was first necessary to develop structurally equivalent bridges which could then be analyzed from an economic and environmental perspective As the goal of this thesis was not to provide detailed construction guidelines for timber bridges, but rather a relative comparison between timber and steel, it was decided that a series of hypothetical structures would be modeled By using conjectural designs, rather than site specific plans, a more general result could be provided This approach also served to significantly reduce the number of potential variables, thus restricting the following analyses to only the most pertinent information Additionally, it should be noted that only the superstructure elements, meaning the deck and

31 feet, giving two 11 foot travel lanes and two 3.5 foot shoulders The center lines of the exterior girders were placed 3.5 feet from the edge of the bridge deck, resulting in a center to center beam spacing of 12 feet Following the general practice of the Vermont Agency of Transportation, a cast in place concrete deck 8.5 inches thick was placed on top of the support girders It was assumed for all calculations that the deck and girders experienced full composite action A three inch thick asphalt wearing surface was assumed to be placed on top of the deck

No sidewalks were supplied, but TL-4 crash rated guardrails conforming to VTrans Standard

S-352 were positioned along the deck edges Standard plans for these guardrails have been included in Appendix D Schematics showing the cross section of the design bridge are provided

in Figures 3a and 3b

Figure 3a: Cross section of the design bridge with steel girders

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Figure 3b: Cross section of the design bridge with glulam girders

To account for a wide variety of potential bridge configurations, the design bridge was modeled in SAP2000 for nine different span lengths ranging from 20 to 100 feet, in 10 foot increments Only the concrete deck and steel or wood girders were included as model elements The asphalt pavement layer and guardrail were both accounted for in the form of applied dead loads The steel sections were assumed to be made from A992 steel while the timber beams were designed using 26F-1.9E southern pine glulams The concrete was taken to have a compressive strength of f′c = 4000 psi The steel and concrete sections utilized built-in properties already defined in SAP2000 However, in order to represent the glulam beams, a new material property needed to be created using the “Define” menu in the SAP workspace This was done by idealizing the timber as an orthotropic material, meaning it has three principle, mutually perpendicular directions along which its properties varied For wood, these are the longitudinal (parallel to the grain), tangential and radial directions The values of the various elastic properties

along these directions were obtained from a table in the 1990 Forest Service publication Timber Bridges: Design, Construction and Maintenance which provided ratios between the different

properties for various wood species These values were also checked against those provided in

the 2010 Forest Products Laboratory Wood Handbook The ratios given for loblolly pine, which

is one of the species comprising the southern pine species group, were used to represent southern pine in general According to the North Carolina State University Tree Improvement Program,

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“[l]oblolly pine is the most commercially important tree species in the southeastern United States, responsible for the majority of the harvested timber.” It is therefore believed that the strength values used can be considered representative of southern pine in general The material properties for steel, concrete and glulam which were used in the models are provided in Tables 1,

2 and 3, below

Table 1: Material Properties of Steel in SAP2000 Model

Property Description SAP2000 Notation Value

Mass Density Mass per unit Volume 15.2297 slugs/ft3

Table 2: Material Properties of Concrete in SAP2000 Model

Property Description SAP2000 Notation Value

Specified Compressive Strength (fʹc) f’c 4 ksi

Mass Density Mass per unit Volume 4.6621 slugs/ft3

Table 3: Material Properties of Southern Pine Glulam in SAP2000 Model

Property Description SAP2000 Notation Value

Longitudinal Modulus of Elasticity (EL) E1 1900 ksi

Tangential Modulus of Elasticity (ET) E2 214.7 ksi

Radial Modulus of Elasticity (ER) E3 150.1 ksi

Longitudinal-Radial Poisson’s Ratio (νLR) U12 33

Longitudinal-Tangential Poisson’s Ratio (νLT) U13 29

Radial-Tangential Poisson’s Ration (νRT) U23 38

Longitudinal Thermal Expansion Coefficient A1 2.0E-6 °F-1

Tangential Thermal Expansion Coefficient A2 1.45E-5 °F-1

Radial Thermal Expansion Coefficient A3 1.92E-5 °F-1

Longitudinal-Tangential Shear Modulus (GLT) G12 153.9 ksi

Longitudinal-Radial Shear Modulus (GLR) G13 153.9 ksi

Radial-Tangential Shear Modulus (GRT) G23 24.7 ksi

Mass Density Mass per unit Volume 1.1189 slugs/ft3

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The deck was modeled as a thin shell having a thickness of 8.5 inches, divided into a

mesh consisting of elements six inches square The mesh was placed at the centroid of the deck

The girders were modeled using frame elements In order to match the resolution of the deck

mesh, each girder actually consisted of a series of six-inch long segments Vertically, these

segments were placed at the centroid of the girder To connect the girder to the deck and model

the composite behavior of the bridge, fictitious joints were used These were located every six

inches along the length of the girder, connecting the nodes of the beam elements with the nodes

of the shell representing the deck The mass and weight of these elements were set to zero, while

the moment of inertia was multiplied by a factor of 1000 to increase their stiffness Doing this

ensured that the forces developed in the concrete deck were fully transferred to the supporting

girders Figure 4 shows an example of the full model, while Figure 5 is a detail of one of the SAP

models showing the interaction between the deck, shell and girder elements

Figure 4: Perspective view of bridge model in SAP2000

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Figure 5: Detail of model showing the deck, girder and fictitious joints

The design of the structural elements of the bridge, namely the girders, followed the

requirements of the 2012 AASHTO LRFD Bridge Design Specifications For the purposes of this

analysis, only the Strength I limit state was considered This limit state includes the effects of the live and dead load but does not consider wind The live load on the bridge was determined using the HL-93 load specified in Section 3.6.1.2 This dictates that two different vehicular loads be analyzed The first is the HS20-44 truck This consists of a three axle truck, with the front axle carrying eight kips and the middle and rear axles each carrying 32 kips The front and middle axles are separated by 14 feet, while the distance between the middle and rear axles is permitted

to vary between 14 and 30 feet so as to produce the worst effect The second design vehicle which must be analyzed is the design tandem This is a vehicle with two axles separated by four feet longitudinally, with both axles supporting 25 kips Both of these design vehicles are to be applied to the bridge concurrently with a uniform load equal to 640 lbs/ft longitudinally, which is

Table 4: Governing Load Cases

Length (ft) Moment (ft-kip) Front Axle Position (ft) Total Length (ft) Moment (ft-kip) Front Axle Position (ft)

It can be seen that for span lengths over 40 feet, the HS20-44 truck will be the governing vehicle

Once the longitudinal positioning of the load was calculated, it was next necessary to position the loads transversely to create the largest impact By observation, it was determined that the exterior girder would be subjected to the greatest force if both the lane load and design vehicle were placed as close to the edge of the deck as permitted by AASHTO Similarly the center girder would experience the largest moment when two trucks and two lane loadings were placed as close to it as allowed Thus, these were the loads applied to the SAP model The lane loads were simply created using an area load of 64 psf across a 10 foot width and along the entire length of the bridge The wheel loads from the design vehicles were slightly more complex According to AASHTO, each axle of the design vehicle produces two wheel loads equal to half

of the axle load This wheel load is to be distributed over an area 20 inches wide (transversely)

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and 10 inches long (longitudinally) to represent the contact area of the tires (200 square inches) However, due to the six inch grid spacing adopted for the bridge deck, it proved impossible to precisely meet that specification Instead, the wheel loads were applied to an area 18 inches wide and 12 inches long (216 square inches) It was felt that this slight discrepancy in contact area would result in negligible differences in results Additionally, it should be noted that the AASHTO specified load is applied at the surface of the deck, while the load applied in the model was located at the deck centroid, 4.25 inches beneath the surface (if the thickness of the asphalt layer is neglected) If the applied surface load is transmitted through the deck along a 45 degree shear plane, than at centroid of the deck, it will actually be distributed over an area 28 inches wide and 18 inches long, or 504 square inches The use of a 216 square inch wheel contact area may thus be conservative at the centroid of the deck

For similar reasons regarding the grid spacing, the axle locations specified in Table 1 could not be exactly replicated in the model The tabulated positions were thus rounded to the nearest half foot in the model, which has the effect of shifting the load centroid closer to the middle of the span by approximately two inches However, this may compensate for a slight discrepancy between the code used to determine the axle locations and the AASHTO specifications The MATLAB code used to calculate axle positions only accounted for the effect

of the design truck or tandem Due to computational limits, it was not feasible to account for the simultaneous application of the truck and lane loads as specified in AASHTO It is known, however, that the maximum moment produced by the lane load would occur at midspan This would have the effect of shifting the total resultant moment from both the truck and the lane load closer to the middle of the bridge, which is precisely what happens when the axle positions specified in Table 4 are rounded to the nearest six inches It is unlikely that this slight shift in location fully compensates for the effect of superpositioning the loads However, given the excess moment capacity observed in the results, it is not believed that this slight discrepancy would have resulted in the selection of different sections Figures 6 – 10, provided below, show the various load patterns applied to the bridges The particular example shown is the 50 foot model with the HS20-44 three axle truck loading, but the other arrangements were fundamentally similar in appearance

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Figure 6: Dead load from railings (326.5 psf, purple) and asphalt (36.25 psf, blue)

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Figure 7: Lane load over the exterior girder shown in blue, 64 psf

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Figure 8: HS20-44 loading over the exterior girder (18.519 psi for the front two wheel

loads, shown in yellow, 74.074 psi for the remaining four, shown in blue)

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Figure 9: Lane load over the center girder (64 psf, blue) In this case there are actually two

10 foot wide lane loads adjoining each other, as permitted by AASHTO to produce the

maximum load effect

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Figure 10: Loads from two HS20-44 trucks over the central girder (four 18.519 psi loads in

yellow and eight 74.074 psi wheel loads in blue)

The goal of creating the model described over the past several paragraphs was to determine the minimum beam size necessary, in both steel and timber, to support the design load

In order for a beam to be sufficient, it had to meet three requirements First, it had to have a depth greater than or equal to 1/30 the span length, as specified by the optional span-to-depth ratios in AASHTO Table 2.5.2.6.3-1 This requirement applied only to the steel beams Second,

it had to have a moment capacity capable of supporting the applied load Third, it had to have a

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total deflection under the unfactored dead load alone of less than L/300 The first two requirements are specified or suggested by AASHTO The third requirement was specific to this project, however While AASHTO no longer specifies mandatory deflection limits for bridges, it does provide recommended values in the event that the owner or designer wishes to incorporate such restrictions However, given that only the primary structural members were modeled in this project and the various transverse stiffeners were neglected, it was felt that the suggested deflection limit of L/800 was too strict A more permissive value of L/300 was therefore adopted The beam depth and deflection limits for each span length as adopted for this analysis are provided in Table 5

Table 5: Beam Depth and Deflection Limits

Span (ft) L/30 Beam Depth Limit (in.) L/300 Deflection Limit (in.)

from the table Section Properties of Structural Glued Laminated Timber published by the AITC

for wood beams It is important to point out here that commercially available wide flange sections were used in the design of the bridges with a steel superstructure These sections are optimized for use in buildings, where it is important to restrict the depth of members for architectural and practical reasons In bridges, where such restrictions are not always necessary, more efficient and lighter weight members can be created through the design of plate girders These tend to be deeper and narrower than commercial sections, resulting in a more efficient use

of material It was determined, however, that the design of plate girder sections was beyond the scope of a preliminary analysis such as this

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Another important point is that with both the steel and the wood superstructures, the same section was used for all three girders This was based on Section 2.5.2.7.1 of the AASHTO LRFD specifications, which states that “[u]nless future widening is virtually inconceivable, the load carrying capacity of exterior beams shall not be less than the load carrying capacity of an interior beam” (AASHTO 2012) Because of this, only the most critical moment created in either the interior or the exterior girder was considered in design

Once the model was run for the initial trial section, the dead load deflection could be immediately checked If the value exceeded L/300, a new section was immediately tried Once deflection was satisfied, the moment capacity of the section was checked As previously stated, it was assumed that both the steel and timber beams, together with the concrete slab, exhibited fully composite behavior The exact mechanisms used to achieve such behavior were not considered and are beyond the scope of this paper

Composite action means that the steel or timber beam acts in concert with a portion of the deck slab to resist the applied moment In essence, a section of the slab serves as an extended flange on the top of the beam, increasing the effective moment of inertia and the moment capacity of the section The portion of the slab which acts in concert with the beam is referred to

as the effective width According to AASHTO Section 4.6.2.6, for the type of bridge design considered here, the effective width may be taken as the tributary area of the girder That means that with girders spaced 12 feet on center and a deck overhang of 3.5 feet, the effective width for the exterior girders is 9.5 feet, while the interior girder has an effective width of 12 feet

Based on that effective width, the trial section selected and the applied moment calculated by the SAP, it could be determined if the section was sufficient using the following

sequence of equations, as adapted from Steel Structures: Design and Behavior by Charles G

Salmon and John E Johnson:

∅𝑐𝐹 (𝑑2 + 𝑡𝑠− 𝑎2) (𝑒𝑞 1)

𝑇 = 𝐴𝑟𝑒𝑞𝐹 (𝑒𝑞 2)